The defeat, after defender Luisao had put Brazil ahead in the 24th minute, left Argentina's chances of reaching the finals in South Africa hanging by a thread.
Midfielder Jesus Datolo replied for Argentina.
Sections of the home crowd chanted Brazil coach Dunga's name in the closing minutes to protest against the impotent tactics of Diego Maradona's Argentina.
"Until the 24th minute, Brazil hadn't even got (to our box). We were very bad on the aerial balls and we paid dearly for that," Maradona told a news conference.
Brazil playmaker Kaka, who came out on top in his duel with Lionel Messi, told Brazilian TV: "Today is a marvellous day, giving this squad added value by guaranteeing our qualification here in Argentina.
"With all the climate that was created (around this match), the team were very intelligent on the pitch."
Brazil's first-half goals came against the run of play as they made their few chances pay while Argentina squandered the lion's share of possession.
From Brazil's kickoff, Argentina won the ball and forced a corner when Carlos Tevez went for a low right cross to the near post and goalkeeper Julio Cesar turned the ball over the goal-line.
Brazil then hit Argentina cold with their first chance when unmarked defender Luisao, the tallest man on the pitch, was allowed to meet Elano's free kick from the right with a header to the far post that beat the diving Mariano Andujar.
Brazil's next real chance also went in after Andujar failed to hold a shot resulting from a Kaka cross from the left, allowing Luis Fabiano to touch the ball home just past the half hour.
Argentina then created a good chance with Julio Cesar saving a shot from Tevez at the near post and Messi's effort from the rebound being cleared off the line.
Maradona made one change at halftime, bringing on striker Sergio Aguero for winger Maxi Rodriguez, but Argentina's tactics of trying to short-pass their way through the middle of the packed Brazil defence remained unchanged.
